Losing money sucks – the mathematics of loss aversion

There’s a lot of research on loss aversion: how bad people feel when they lose $50 vs. how good they feel good about gaining $50. This research is kind of taking an absolute value of emotion, positive or negative. We can represent this with emoji equations:

😀 == 😫 (large-magnitude happiness or sadness)

🙂 == 🙁 (small-magnitude happiness or sadness)

😫 > 🙂 > 😐 (ordering magnitude of emotion)

What research has shown is that, when someone loses $X and feels 😫 (large-magnitude), if they gain $X they feel 🙂 (small-magnitude). Gaining money doesn’t make them as happy as losing money makes them sad!

My hypothesis is that people have an intuitive feeling about the math behind these experiments and the results make a lot of sense if you look at percentages instead of values.

For example, suppose you invest $100 and your investment goes up to $150. Holding that money in your hand, $100 is a distant memory, when you had 33% less than you currently have. ($150 – (33%*$150) = $100)

Now let’s say your investment doesn’t do well and you’re standing there with $50, feeling sad. Now you have 50% of what you started with.

My hypothesis is that loss aversion is really an intuition about the difference between 33% and 50%. My guess is that the emoji magnitude would be (roughly) equal if you gained and lost the same percentage. E.g., these would have equal magnitudes of satisfaction:

Loser

Winner

33% plan

$67 🙁

$150 🙂

50% plan

$50 😫

$200 😀

If we extend this out to an infinite number of plans, we can see it breaks down at the ends. I don’t think losing 80% would feel the same magnitude as making 4x, but it also feels hard to imagine. Losing 80% of a meaningful amount of money would feel terrible, but would it feel as terrible as 4x-ing my money feels good? 10x-ing? 10x feels more significant than 4x, but 4x-5x? I’m not sure I’d be materially cockier.

Anyway, I assume the ratios are a bit different for different people. But it always struck me with the loss aversion studies that most people understand that going from $1 to $2 doubles your money, but going from $2 to $3 does less.